Present Value

The current worth of a future sum of money or cash flow stream, found by discounting each future amount using a specified discount rate.

Source: Brealey, Myers & Allen 2019

Each future amount is divided by one plus the discount rate raised to the power of the number of periods until it occurs, and the results are summed across the stream. The effect is that amounts arriving later are reduced more heavily, and the reduction compounds, so a sum due in twenty years contributes far less than one due in two. The calculation requires the amounts, their timing and the rate, and the last of these is usually the assumption on which the result most depends. The first period is conventionally left undiscounted, and where flows accrue continuously through a period a mid-year adjustment is sometimes applied, which matters more over long horizons.

Source: Brealey, Myers & Allen 2019

Because costs and health effects arrive at different times and cannot be added until they are expressed at a common point. Converting everything to present value allows a stream of flows over decades to be summarised as a single figure that can be compared across options. Without it, an intervention incurring cost now and producing benefit later would be compared with one doing the reverse using quantities that are not commensurate. It is also the operation underlying net benefit, since converting health and cost to a common point in time is a precondition for combining them at all.

Source: Drummond et al. 2015

They are inverse operations using the same rate. Present value moves an amount backward in time by discounting; future value moves it forward by compounding. Economic evaluation works almost entirely in present value, since the decision is taken now and flows arriving later must be brought to that point. Future value is used mainly where the question concerns what a fund will accumulate to rather than what a future obligation is worth today. The distinction matters in practice because a fund accumulating to meet a future liability is assessed on future value while the liability itself is valued in present terms.

Source: Brealey, Myers & Allen 2019

The discount rate, since its effect compounds with the horizon and a modest change can alter the sign of a net figure for a project whose returns arrive late. This is why analyses report results across a range of rates rather than at a single value, and why the rate applied in public appraisal is specified centrally rather than chosen by the analyst. Over long horizons the rate frequently does more work than any other input. Discounting health raises separate questions from discounting money, since health cannot be invested, and frameworks differ on whether the same rate should apply to both.

Source: HM Treasury, The Green Book 2022

The discount rate applied, the year treated as the present, and the horizon over which flows were counted, since the figure is uninterpretable without them. Undiscounted totals should be reported alongside where the horizon is long, since the difference between them shows how much the result depends on the rate. Where costs are in constant prices, that should be stated, since applying a nominal rate to real values compounds an error over the whole period. Where the horizon extends beyond the period for which evidence exists, the point at which observation stops and projection begins should also be identified.

Source: Drummond et al. 2015